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HIAS-E-41
Expected Inflation Regimes in JapanTatsuyoshi Okimoto
Australian National University
RIETI
January 2017
Hitotsubashi Institute for Advanced Study, Hitotsubashi University2-1, Naka, Kunitachi, Tokyo 186-8601, Japan
tel:+81 42 580 8604 http://hias.ad.hit-u.ac.jp/
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Expected Inflation Regimes in Japan
⇤
Tatsuyoshi Okimoto†
Australian National University and RIETI
January 2017
Abstract
This paper examines the dynamics of expected inflation regimes in Japan overthe last three decades based on the smooth transition Phillips curve model. We findthat there is a strong connection between the expected inflation and monetary policyregimes. The results also suggest that the introduction of the inflation targeting pol-icy, and quantitative and qualitative easing in the beginning of 2013 have successfullyescaped from the deflationary regime, but was not enough to achieve the 2% inflationtarget. Finally, our results indicate the significance of exchange rates in explaining therecent fluctuations of inflation, and the importance of oil and stock prices in maintain-ing the positive expected inflation regime.
JEL codes: C22, E31, E52Key words: Hybrid Phillips curve, monetary policy, inflation targeting, qualitative andquantitative easing, smooth transition model
⇤The author thanks participants at ESRI International Conference and CEM Workshop, and seminarparticipants at RIETI, Waseda University, ANU, Hitotsubashi University, and Keio University for their help-ful comments. The author also thanks Hitotsubashi Institute for Advanced Studies (HIAS) at HitotsubashiUniversity for their support and hospitality during his stay. All remaining errors are mine.
†Associate Professor, Crawford School of Public Policy, Australian National University and Visiting Fellow,Research Institute of Economy, Trade, and Industry (RIETI), 132 Lennox Crossing, ANU, Acton, ACT 2601,Australia. Tel: +61-2-6125-4763. Email: [email protected].
1 Introduction
Inflation is obviously one of the most important variables for macroeconomists, practitioners,
and policy makers, since inflation a↵ects the value of money. As a result, inflation rates
significantly influence the behaviors of individuals and firms. Therefore, the central banks
and monetary authorities have paid special attention to the inflation rates recently, and
inflation-targeting monetary policy has been adopted by more than 20 countries including
US and UK. As for Japan, the first arrow in the first stage of Abenomics is to conduct an
aggressive monetary policy; as part of this, the Bank of Japan (BOJ) introduced the inflation
targeting policy in January 2013 by committing a 2% price stability target. Following this
introduction, the BOJ has conducted innovative monetary policies, including the quantitative
and qualitative easing (QQE) and negative interest policies. Nonetheless, it is still uncertain
whether and when the 2% price stability target will be achieved.
To achieve this inflation target, one of the crucial indicators is expected inflation, which is
expected inflation level for the future by individuals and firms.1 Since inflation is anticipated
to approach the expected inflation in the future, aside from the short-term fluctuations along
with the business cycles, it can provide a useful measure to evaluate the appropriateness of
the current monetary policy as well as the necessity of additional monetary easing to achieve
the inflation target. Therefore, it is extremely informative to examine the current expected
inflation level and compare it with the inflation target set by the monetary authorities.
The purpose of this paper is to investigate the dynamics of expected inflation in Japan
over the last three decades and their relationship with monetary policies. Over the last three
decades, Japanese economy has experienced many significant events, such as the bursting
of the bubble economy, the lost two decades, the Lehman and Euro financial crises, and
the introduction of a zero interest rate and inflation targeting monetary policies. It is quite
meaningful to empirically study how expected inflation rates in Japan have evolved through
these events. In particular, the Japanese economy su↵ered from low expected inflation due
to the deflationary mind formulated through what we call the lost two decades after the
bursting of the bubble economy in 1990. It is important to examine whether the expected
inflation during this period is indeed below zero or not and how the BOJ’s policies during
this period, such as the zero interest and quantitative easing policies, a↵ected the expected
inflation. In addition, it is of great interest to analyze whether and how the expected inflation
has become closer to the BOJ’s 2% target since the BOJ introduced the QQE.
1Precisely speaking, there are many types of expected inflation depending on the definition of the futureas well as the economic agent. The expected inflation analyzed in this paper is the expected inflation in thedistant future by the mathematical definition. However, judging from the results of the analysis, there shouldbe no substantial di↵erence from the expected inflation over the next 5 or 10 years. In addition, since we usethe inflation based on the consumer price index, the expected inflation for this paper is naturally consideredto be the one by households.
One of the di�culties in assessing the dynamics of expected inflation is that expected
inflation is unobservable. Although survey-based expected inflation rates have recently be-
come available due to the development of survey data, it is often pointed out that surveyees
are mostly limited to professionals, and survey expected inflation contains various possible
biases. For example, Fuhrer, Olivei, and Tootell (2012) attempt to estimate the expected
inflation rates in Japan based on the survey data, but their estimates uniformly exceed the
actual inflation rates between the beginning of 1990 and 2010. Therefore, it is not straight-
forward to consider that the survey expected inflation to be unbiased estimates of expected
inflation. In addition, it is not easy to estimate the expected inflation rates from the survey
data, either.
To overcome the problem associated with the survey data, many recent studies have tried
to estimate the expected inflation rates by modeling them as unobservable state variables and
estimating them based on the macroeconometric models. In this vein, this paper estimates
the expected inflation rates in Japan using the hybrid Phillips curve. More specifically,
we introduce regime switching to the Phillips curve to capture the regime shifts in expected
inflation rates,2 following Kaihatsu and Nakajima (2015). They employ the Markov-switching
(MS) model to examine the possible regime changes in expected inflation, but their MS model
is stationary. Therefore, the regime distribution will converge on the stationary distribution
in the long-run, meaning that their MS model cannot capture a permanent regime change in
expected inflation. However, it is likely that there are permanent regime changes in expected
inflation given the experiences of the Japanese economy over the last three decades, including
the bursting of the bubble economy and significant changes in monetary policies.
To capture the possible permanent regime changes in expected inflation rates, we apply
the smooth-transition (ST) model to the hybrid Phillips curve. By doing so, we attempt
to identify the number of regimes, characterize each regime, and estimate the dynamics of
expected inflation. More specifically, we address the following questions: (i) How many
expected inflation regimes were there over the last three decades in Japan? (ii) Is there
any relationship between inflation regimes and monetary policy regimes? (iii) What were the
expected inflation rates under each inflation regime? (iv)Has the expected inflation increased
after the adoption of inflation targeting policy by BOJ? (v)Is the current expected inflation
significantly di↵erent from the BOJ’s target of 2%? (vi)What are the e↵ects of oil prices,
stock prices, and exchange rates on Japanese inflation?
Our findings can be summarized as follows. First, there have been three regimes in
expected inflation in Japan over the last three decades, and they reasonably corresponded to
the traditional monetary policy regime between 1985 and 1994 (regime 1), the extremely low
interest rate monetary policy regime between 1995 and 2012 (regime 2), and the inflation
2In this paper, we use the regime to express the state, and both terms are used interchangeably.
targeting monetary policy regime since 2013 (regime 3).
Second, based on the three-regime ST Phillips curve model, each regime can be charac-
terized as follows. The expected inflation in regime 1 was relatively high and stable at 1.5%
for the core inflation and 2.0% for the core2 inflation.3 In regime 2, the expected inflation
decreased considerably to �0.20% for the core inflation and to �0.61% for the core2 inflation.
While the estimate of expected inflation was not significantly di↵erent from 0 for the core
inflation, it was significantly negative for the core2 inflation. In addition, our results show
that the expected inflation had been stable at below zero during this regime, although the
BOJ enacted many pioneering monetary policies, such as a zero interest rate and quantitative
easing monetary policies. Thus, our results suggest that those BOJ’s monetary policies were
not enough to escape from the deflationary regime, although they most likely supported the
Japanese economy and prevented the expected inflation from further decreases. Finally, the
expected inflation in regime 3 showed a sizable increase to 0.34% for the core inflation and
0.48% for the core2 inflation. While the estimate of expected inflation was not significantly
di↵erent from 0 for the core inflation, it was significantly positive for the core2 inflation.
More importantly, our results clearly demonstrate that the expected inflation in regime 3 is
significantly smaller than the BOJ’s 2% inflation target for both inflation measures. Thus,
the QQE and the negative interest policies conducted in regime 3 were partially successful
for escaping from the deflationary regime, but they were not su�cient to achieve the BOJ’s
2% inflation target.
Third, we extended the benchmark model so that the oil prices, stock prices, and exchange
rates could a↵ect inflation. Here, our results indicate that the oil price and exchange rate
had a relatively large e↵ect on the core inflation in regime 2 and regime 3, respectively. On
the other hand, the oil prices, stock prices, and exchange rates had little e↵ect on the core2
inflation in regimes 2, although the exchange rates became influential in regime 3. Thus, our
results suggest that the depreciation of Japanese yen occurred with the introduction of the
inflation targeting policy by the BOJ played an important role in the significant increase of
inflation in 2013.
Finally, we consider another type of extended model in which the oil prices, stock prices,
and exchange rates could a↵ect the dynamics of the expected inflation regime. Our results
show that the oil and stock prices had significant impacts on the expected inflation regime
for the core inflation, while the stock price strongly a↵ected the expected inflation regime for
the core2 inflation. This greatly contrasts with the above results, showing the importance
of the exchange rates to explain the realization of inflation. More specifically, our results
demonstrate that, even after 2012, the expected inflation regime tended to move back to the
3In this paper, we calculate two measures of inflations from the consumer price index (CPI). More precisely,the core inflation is calculated from the headline CPI, excluding fresh food; the core2 inflation is calculatedfrom the headline CPI, excluding food and energy. See Section 3.1 for more details.
deflationary regime when the oil or stock prices decrease. Therefore, the BOJ’s purchase of
Exchange Traded Funds (ETF) could be e↵ective in preventing the expected inflation from
going back to the deflationary regime, which was mainly observed before 2012.
The remainder of this paper is organized as follows. Section 2 introduces the ST Phillips
curve model and explains how to choose the number of regimes. Section 3 summarizes the
empirical results based on the benchmark model, while Section 4 provides the empirical
results based on the extended models. Finally, Section 5 concludes the paper.
2 Methodology
This paper employs the hybrid Phillips curve model with regime switching to estimate the
dynamics of the expected inflation rates in Japan, following Kaihatsu and Nakajima (2015).
They apply the MS model to capture the possible regime changes in expected inflation.
In the Markov-switching model’s framework, the expected inflation dynamics are typically
modeled by a stationary Markov process; hence, the expected value of expected inflation is
constant. Although it is possible for the expected inflation to deviate from its expected level
temporarily, it has to revert to the stationary level eventually. In this sense, the MS Phillips
curve model cannot capture permanent regime changes in the expected inflation.4 However,
it is likely that there are permanent regime changes in the expected inflation, for example,
after drastic changes to the monetary policies. Therefore, we adopt the ST Phillips curve
model to capture the possible permanent regime changes in the expected inflation rates. By
doing so, we try to find the answers to the questions addressed in Introduction.
2.1 ST Phillips Curve Model
The ST model is developed within the autoregressive model by, among others, Chan and
Tong (1986), and Granger and Terasvirta (1993); its statistical inference is established by
Terasvirta (1994). Since then, the ST model has been applied to many types of models.
However, to our best knowledge, none of the studies use the ST Phillips curve model to
estimate the regime shifts in expected inflation. In this subsection, we briefly discuss our
model.
To examine the regime shifts in expected inflation in Japan, our benchmark model is
a hybrid Phillips curve.5 One of the most important characteristics of the hybrid Phillips
curve is that the current inflation rate depends not only on the current output gap and
expected inflation but also the past inflation rates. Assuming that the expected inflation
4By imposing zero restrictions on the transition probabilities, the MS model can also capture permanentregime changes. However, we still prefer the ST model, since it allows regimes to change slowly from one toanother while the MS model assumes the regime changes occur all of sudden in one period.
5See Fuhrer and Moore (1995), Roberts (1997), Galı and Gertler (1999), Galı, Gertler, and Lopez-Salido(2005) for details on the hybrid Phillips curve.
rate is constant, it is given as
⇡t =KX
k=1
↵k⇡t�k +
1�
KX
k=1
↵k
!µ+ �xt + "t. (1)
Here, ⇡t is an inflation rate at time t, and xt is an output gap. If the inflation is persistent
partially due to the backward-looking price setting by firms, the past high inflation tends
to be followed by relatively high current inflations. The hybrid Phillips curve (1) explicitly
models this possibility and can be considered to be the autoregressive (AR) model with an
exogenous variable, assuming that the output gap is exogenous. If the output gap stays
stationary level at 0 and the AR coe�cients in (1) satisfy the stationarity conditions,6 it is
easy to confirm that
limh!1
Et(⇡t+h) = µ.
Here, Et(·) is a conditional expectation given the information available at time t. Therefore,
we can interpret µ as the expected inflation at time t
Over the past three decades, the Japanese economy has experienced many significant
events, such as a bursting of the bubble economy, the lost two decades, the Lehman and Euro
financial crises, and the introduction of a zero interest rate and inflation targeting monetary
policies. As a result, it is likely that the expected inflation in Japan has had regime shifts
over the last thirty years. In this paper, we investigate this possibility by modeling regime
changes as permanent regime shifts. More specifically, we apply the ST model to the hybrid
Phillips curve (1) so that the expected inflation has regime shifts as
µt = µ(1) +G(st; c, �)�µ(2) � µ(1)
�. (2)
Here G(·) is called a transition function taking the values between 0 and 1, and st is called a
transition variable. If the current regime continues forever or the transition function G takes
the same value forever, it can be easily shown that
limh!1
Et(⇡t+h) = µt.
In this sense, µt can be regarded as the expected inflation at time t. If G(st) in (2) is equal
to 0, µt = µ(1), while G(st) = 1 implies µt = µ(2). Thus, the expected inflation modeled as
(2) is assumed to have two regimes characterized by µ(1) and µ(2), and it generally takes the
value between them depending on the value of the transition function G.
The transition function and transition variable are determined according to the purpose of
analysis. For example, Lin and Terasvirta (1994) investigate a continuous permanent regime
6Stationary conditions for AR models are that the absolute values of all roots of the AR characteristicequation
1� ↵1z � · · ·� ↵KzK = 0
are larger than 1.
change using the logistic transition function with a time-trend transition variable. Since the
purpose of this paper is to detect the possible permanent regime shifts in expected inflation
in Japan over the last three decades, we follow their research, and use a logistic transition
function given as
G(st; c, �) =1
1 + exp���(st � c)
� , � > 0. (3)
Here, c is a location parameter determining the timing of the transition, and � is a smooth-
ness parameter capturing the speed of the transition. One of the advantages of the logistic
transition function is that it can express various forms of transitions depending on the values
of c and �. Additionally, c and � can be estimated from the data, enabling the selection of
the best transition patterns based on data, which is very attractive for the purposes of this
paper, particularly examining the regimes shifts in expected inflation.
Finally, we use a time trend st = t/T as the transition variable, following Lin and
Terasvirta (1994), where T is the sample size. In addition, we assume 0.05 < c < 0.95
so that we can detect the regime shifts in expected inflation within the sample period. In
this setting, G(st) takes the value close to zero with smaller st around the beginning of the
sample period, making µt close to µ(1). Therefore, µ(1) can be considered to be the expected
inflation around the beginning of the sample. In contrast, around the end of the sample, µt
approaches µ(2) as G(st) approaches one with a larger st. Thus, µ(2) can be considered to be
the expected inflation around the end of the sample. Specifically, under these assumptions,
the expected inflation µt changes from µ(1) to µ(2) with time as G(st) changes from zero to
one. By estimating the model, we can identify not only the expected inflation levels of two
regimes, µ(1) and µ(2), but we can also identify the timing and speed of the change from µ(1)
to µ(2).
Furthermore, we can extend the two-regime model (2) to models with three or more
regimes. For example, the three-regime model can be written as
µt = µ(1) +G1(st; c1, �1)�µ(2) � µ(1)
�+G2(st; c2, �2)
�µ(3) � µ(2)
�, (4)
Here, Gi, i = 1, 2 is the logistic transition function (2), and we assume c1 < c2. In this
model, when st is near 0 or around the beginning of the sample, µt approaches the expected
inflation of the first regime, µ(1), because both G1(st) and G2(st) take small values near 0.
When c1 < st < c2, µt becomes close to the expected inflation of the second regime, µ2;
this is because G1(st) tends to be near one, but G2(st) tends to be near zero. Finally, when
c2 < st, µt is close to µ(3) with G1(st) and G2(st) taking values near one. Thus, under this
specification, the expected inflation µt changes from µ(1) via µ(2) to µ(3) with time as first
G1(st) changes from zero to one; this is followed by a similar change in G2(st). The extent
to which the expected inflation is close to each regime’s expected inflation, and the way in
which it becomes close, depends on the values of ci and �i, which can be estimated from data.
This makes the multiple-regime ST model attractive for the examination of the dynamics of
expected inflation in Japan
A number of recent studies have pointed out that the flattening of the Phillips curve (1)
has been promoted in advanced countries. For instance, Roberts (2006) reports that the US
Phillis curve has been flattened since 1980s and that the changes in monetary policy have
played an important role in this flattening. Similarly, De Veirman (2009) and Fuhrer, Olivei,
and Tootell (2012) document that the Phillips curve has been flattened in Japan since the
early 1990s. Therefore, it is quite relevant to consider the time variation in the slope of the
Phillips curve expressed by �. Similar to µt, we model �t using the ST model. For example,
the three-regime model is specifically given as
�t = �(1) +G1(st; c1, �1)��(2) � �(1)
�+G2(st; c2, �2)
��(3) � �(2)
�(5)
Here, we assume that the transition functions, G1 and G2, in (4) and (5) share the same
parameters of ci and �i. In other words, it is assumed that the timing and speed of regime
transitions in µ and � are the same. However, note that this assumption is not that restrictive,
since the actual dynamics could be very di↵erent due to the di↵erent estimates of µ(i) and
�(i) for each regime.
In sum, the ST Phillips curve model in this paper is given by
⇡t =KX
k=1
↵k⇡t�k +
1�
KX
k=1
↵k
!µt + �txt + "t. (6)
In addition, µt and �t are modeled with the ST model such as (4) and (5).
2.2 Choice of number of regimes
The choice of the number of regimes is crucial for the ST model. As previously discussed,
over the last three decades the Japanese economy has experienced many significant events,
such as the bursting of the bubble economy, and the introduction of zero interest rate and
inflation targeting monetary policies. As a result, it is likely for the expected inflation in
Japan to have had several regime shifts over the last three decades, but there is no guidance
about the number of regime. Hence, it is important to specify the number of regimes. In this
paper, we choose the number of regimes based on hypothesis testing, which can compare the
models with the M and M + 1 regimes. In this subsection, we briefly discuss those tests.
First, we test the one-regime Phillips curve model (1) against the two-regime Phillips
curve model, which is characterized by (2) and (6). In this case, the null hypothesis and the
alternative hypothesis can be expressed as H0 : � = 0 and H1 : � > 0, respectively. However,
this test is not standard since parameters µ(i) and �(i), i = 1, 2 cannot be identified under
the H0.7
To deal with this identification problem, Luukkonen, Saikkonen, and Terasvirta (1988)
suggest approximating the logistic function with a first-order Taylor approximation around
� = 0. This results in the auxiliary regression of the form
⇡t =KX
k=1
ak⇡t�k + b0 + b1xt + b2st + b3xtst + et. (7)
Luukkonen, Saikkonen, and Terasvirta (1988) show that testing H0 : � = 0 in the two-regime
Phillips curve model (2), (6) is equivalent to testing H 00 : b2 = b3 = 0 in the auxiliary
regression (7). Since there is no identification problem in this auxiliary regression, we can
easily test the null hypothesis H 00 : b2 = b3 = 0. Specifically, Luukkonen, Saikkonen, and
Terasvirta (1988) demonstrate that the Lagrange-multiplier (LM) test statistic to test H 00
asymptotically follow the Chi-squared distribution with 2 degree of freedom. Based on their
results, we can test the one-regime model against the two-regime model.
Furthermore, Eitrheim and Terasvirta (1996) develop the LM statistic to test the M -
regime model against the alternative of the M+1 regime model based on the similar auxiliary
regression model. Therefore, Based on their results, we can test, for example, the two-regime
model against the three-regime model.
3 Empirical Analysis
In this and the following sections, we discuss our empirical results. Specifically, based on
the empirical analysis we address the following questions: (i) How many expected inflation
regimes were there over the last three decades in Japan? (ii) Is there any relationship between
inflation regimes and monetary policy regimes? (iii) What were the expected inflation rates
under each inflation regime? (iv) Has the expected inflation increased after the adoption of
the inflation targeting policy by the BOJ? (v) Is the current expected inflation significantly
di↵erent from the BOJ’s target of 2%? (vi) What are the e↵ects of oil prices, stock prices,
and exchange rates on Japanese inflation?
3.1 Data
Our empirical analysis is based on the Japanese monthly data of CPI, industrial production
index, nominal e↵ective exchanger rate, oil prices, and stock prices, with the sample period
lasting from January 1985 to July 2016. We use two measures for CPI, namely the CPI
excluding fresh food and the CPI excluding food and energy. Both data are downloaded
7If we express the null hypotheses as H0 : µ(1) = µ(2), �(1) = �(2), then there is still an identificationissue, since we cannot identify � and c.
from the Ministry of Internal A↵airs and Communications, and they are seasonally adjusted
by the X-12-ARIMA method. The seasonally adjusted industrial production is obtained from
the Ministry of Economy, Trade, and Industry, while the nominal e↵ective exchange rate is
downloaded from the BOJ. For the oil price, we use the oil price index obtained from the
International Monetary Fund. Finally we collect the TOKYO Price Index (TOPIX) from
the Datastream for the stock price.
We calculate the inflation rate by taking the first di↵erence of log of CPI measures and
multiplying them 1200 to annualize. Thus, the inflation rate at time t, ⇡t, is calculated as
⇡t = 1200(log pt � log pt�1),
where pt is a CPI measure at time t.8 We call the inflation based on the CPI excluding fresh
food the core inflation, and the CPI excluding food and energy core2 inflation.9
Finally, the output gap is calculated by taking the di↵erence between the industrial
production and its trend calculated by the Hodrick-Prescott filter.10
3.2 Choice of Number of Regimes
The purpose of this paper is to investigate the dynamics of expected inflation in Japan over
the last three decades and their relationship to monetary policy. To this end, we employ the
ST Phillips curve (6) to detect the regime shifts in expected inflation. In this subsection, we
select the number of regimes by the sequential testing based on Luukkonen, Saikkonen, and
Terasvirta (1988) and Eitrheim and Terasvirta (1996), as discussed in the previous section.
The second and third rows of Table 1 summarize the results of hypothesis testing of
the one-regime model against the two-regime model based on Luukkonen, Saikkonen, and
Terasvirta (1988).11 The second row shows the values of their proposed LM statistic, and
the third row reports their p-values. As can be seen, the LM statistic takes large values with
small p-values for both inflation measures. Thus, the one-regime model is obviously rejected
against the two-regime model, meaning that there is at least one regime shift in Japanese
inflation regimes.
[Insert table 1 here]
8During the sample period, the consumption tax rate changed three times in April 1989, April 1997, andApril 2014. In this paper, we assume that the consumption tax hikes are fully reflected within one month, andwe adjust them by linearly interpolating the data of April from the data in March and May in the concernedyear. Rigorously speaking, there are some goods, such as public utility charges, that reflect the consumptiontax hike with more than a one-month delay. However, the proportion of those goods is relatively small andshould not a↵ect the estimation results.
9Note that for many countries, including US, the core inflation typically means the core2 inflation in thispaper. Note also that the core inflation is the BOJ’s o�cial measure for the 2% inflation target.
10More precisely, we normalize it to have zero mean and unit variance.11We set K = 2 in (6) for the rest of the analysis, since the higher order AR terms are not significant.
Next, we test the two-regime model against the three-regime model based on Eitrheim and
Terasvirta (1996). The results are shown in the fourth and fifth rows of Table 1, indicating
the great contrast between the two inflation measures. For the core inflation, the two-regime
model is preferred to the three-regime model with a large p-value of 0.46. However, for the
core2 inflation, the two-regime model is rejected against the three-regime model with less
than 5% p-value.
Finally, the last two columns of Table 1 report the results of the hypothesis testing of the
three-regime model against the four-regime model. The relatively large p-values suggest that
there is no evidence of the four-regime model over the three-regime model for both measures.
In sum, our results demonstrate that the two-regime model is preferred for core inflation,
while the three-regime model is dominant for core2 inflation. In other words, it is enough to
consider three regimes in expected inflation over the last three decades in Japan. For this
reason and to make the results comparable between two inflation measures, we will use the
three-regime ST Phillips curve characterized by (4)-(6) for both measures in the following
analysis.
3.3 Inflation Regimes and Monetary Policy Regimes
In this subsection, we show the estimated regime transition dynamics to see when and how
the regime shifts in the three-regime ST Phillips curve model (4)-(6) have occurred over the
last three decades.
We estimate the three-regime ST Phillips curve model via the maximum likelihood estima-
tion (MLE), assuming that "t independently and identically follows the Normal distribution
with the mean of 0 and variance of �2. We also impose the restrictions that the coe�cients
on the output gap are nonnegative in order to be consistent with the economic theory.12 The
estimation results are documented in Table 2.13 For the core inflation, c1 is estimated to be
0.29, meaning that the center of the transition from regime 1 to regime 2 is estimated to
be around June 1994. In addition, the estimate of �1 of 200 indicates that the speed of the
transition is very rapid. To see this point graphically, Figure 1 plots the estimated dynamics
of the transition functions G1(st) and G2(st). As can be seen, for the core inflation, G1 has
been almost 0 until the end of 1993, but it increased rapidly to 1 during 1994 and has been 1
since the beginning of 1995. For the core2 inflation, c1 is estimated as 0.35, suggesting that
the center of transition is around March 2006. The speed of the transition is estimated to
be relatively slow with a �1 estimate of 19.1. As a result, G1 for the core2 inflation changes
12If these restrictions are bound for some coe�cients, we replace them with 0 and re-estimate the model.13If the transition function looks like a step function, the estimate of �i becomes very large and is not
well determined, since the log-likelihood becomes insensitive with �i. In these cases, we have fixed �i at anupper bound equal to 200 and have re-estimated the model. In this case, the parameter’s standard errors aredenoted by NA.
from 0 to 1 relatively smoothly between 1994 and 1998, as can be confirmed from Figure 1.
[Insert Table 2 and Figure 1 here]
Regarding c2 and �2, both inflation measures show quite similar estimation results. c2 is
estimated to be 0.88 and 0.89 for the core and core2 inflation, respectively. In other words,
the estimation results indicate that the center of the transition from regime 2 to regime 3 is
around September 2012 and February 2013 for each measure, respectively. In addition, �2 is
estimated to be 200 for both measures, meaning that the speed of transition is very rapid.
These results can be also verified from the estimated dynamics of G2, which are plotted in
Figure 1.
In sum, our results suggest that the first regime shift occurred at around 1995, although
the speed of transition depended on the measure of inflation. The BOJ had conducted the
traditional monetary policy using the bank rate as a policy rate before 1995. However, the
liberalization of interest rates was completed in October 1994, and the direct relationship
between the bank rate and deposit interest rate has disappeared. Following these events, the
BOJ adopted the call rate as a new policy rate in March 1995. Then, the BOJ started the
extremely low interest rate policy with the 0.5% call rate in September 1995. Thus, there
were significant changes to the BOJ’s monetary policy in 1995. Indeed, previous studies,
such as Miyao (2000) and Inoue and Okimoto (2008), detect a regime shift in the e↵ect
of Japanese monetary policy around this period. Interestingly, the first regime shift in the
three-regime Phillips curve seems to coincide with this timing.
The second regime shift took place at around the beginning of 2013, and it occurred very
rapidly. The BOJ introduced the inflation targeting policy in January 2013 by committing
to a 2% price stability target. Following the introduction, the BOJ launched the QQE in
April 2013. Obviously, the second regime shift in the three-regime Phillips curve corresponds
to these changes.
Thus, there seems to be strong relationship between the inflation regimes and monetary
policy regimes in Japan over the last three decades. Specifically, the first inflation regime
is characterized by the conventional monetary policy regime. The second inflation regime
roughly corresponds to the low or zero interest rate monetary policy regime. The third
inflation regime coincides with the inflation targeting monetary policy regime.
3.4 Expected Inflation Regimes
The previous subsection demonstrated the strong correspondence between the inflation regime
and monetary policy regime. In this subsection, we investigate how the expected inflation
and slope of the Phillips curve varied through the regime changes, focusing on the expected
inflation.
Figure 2 plots the estimated dynamics of the expected inflation and slope of the Phillips
curve based on the three-regime ST Phillips curve model (4)-(6). As can be seen, the expected
inflation has changed significantly depending on the regimes. In particular, the expected
inflation dropped considerably in regime 2 for both inflation measures with some rebound in
regime 3. Similarly, the slope of the Phillips curve greatly decreased in regime 2, followed
by no change in the core inflation and a further decline in the core2 inflation. This is
generally consistent with the recent finding of flattening of the Phillips curve in Japan, which
is documented by, among others, De Veirman (2009) and Fuhrer, Olivei, and Tootell (2012).
The results also indicate that no shift in the slope of the Phillips curve in regime 3 is the
main reason why the two-regime model is preferred for the core inflation. In other words,
the results suggest that there were arguably three regimes in the expected inflation for both
inflation measures.
[Insert Figure 2 here]
Next, we characterize each expected inflation regime more precisely based on the esti-
mates reported in Table 2. As can be seen in Table 2, the expected inflation in regime 1 is
significantly positive with estimates of 1.5% and 1.9% for core and core2 inflations, respec-
tively. In addition, as confirmed by Figure 2, the expected inflation had been stable until
at least 1993. Thus, regime 1 is characterized by relatively high stable inflation for both
inflation measures.
In contrast, the expected inflation in regime 2 is negatively estimated for both measures.
More precisely, the expected core inflation in regime 2 is estimated to be �0.20, but it is not
significantly negative. As a result, the expected core inflation showed a significant decrease
at around 1995; it was then stable until the end of 2012. On the other hand, the expected
core2 inflation in regime 2 is estimated significantly negatively with an estimate of �0.61.
As can be seen from Figure 2, the expected core2 inflation changed smoothly from 1.9% to
�0.61% between 1994 and 1998, and it stayed the same until the end of 2012. In the 2000s,
the BOJ enacted innovative monetary policies, such as the zero interest rate and quantitative
easing monetary policies. However, our results indicate that these policies were not enough
to keep or recover the positive expected inflation, although they might prevent the expected
inflation from decreasing further.
Finally, the expected core inflation in regime 3 is estimated positively, but it is insignifi-
cantly di↵erent from 0 with an estimate of 0.34%. As a result, the core inflation jumped up
from �0.20% to 0.34% in the beginning of 2013, as can be seen in Figure 2. In contrast, the
estimate of the expected core2 inflation in regime 3 is significantly positive with an estimate
of 0.47. As a result, the core2 inflation had a sizable rapid increase from �0.61% to 0.47%
in the beginning of 2013, as confirmed in Figure 2. However, compared with the BOJ’s 2%
inflation target, the expected inflation in regime 3 is significantly smaller for both inflation
measures. Thus, our results suggest that the BOJ’s policies after the introduction of the 2%
inflation target, such as QQE and the negative interest policies, are partially successful for
escaping from the deflationary regime, but they are not su�cient to achieve the BOJ’s 2%
inflation target.
4 Results of the Extended Model
Analyses thus far have been based on the hybrid Phillips curve (6). In this model, the current
inflation rate is determined by the past inflation rates and the current output gap. However,
it is likely that inflation in Japan depends on other variables, such as oil prices, stock prices,
and exchange rates. For example, a rise in inflation was observed after the introduction
of the 2% inflation target by the BOJ, which is partly due to the increase in the expected
inflation, as we confirmed the previous section. However, it is plausible that price increases
in import goods due to the depreciation of yen also played some role. In addition, it is
often argued that the recent Japanese inflation was suppressed by a decline in oil prices as a
result of the stagnation of the emerging economy, particularly China, and the oversupply by
oil producing countries. Indeed, previous studies, such as Hooker (2002) and Hara, Hiraki,
and Ichise (2015), have proposed the Phillips curve, including the oil prices and exchange
rates. Furthermore, it is conceivable that the stock prices could a↵ect inflation, particularly
expected inflation. Following these observations, in this section we extend the benchmark
model of the previous section to accommodate the oil prices, stock prices, and exchange rates
to see their e↵ects on the inflation and check the robustness of the results of the previous
section.
4.1 Extended Phillips Curve
In this subsection, we examine the e↵ects of the oil prices, stock prices, and exchange rates
by employing the extended three-state Phillips curve model including these variables. Specif-
ically, following Hooker (2002) and Hara, Hiraki, and Ichise (2015), we consider the following
extended Phillips curve:14
⇡t =KX
k=1
↵k⇡t�k + (1�KX
k=1
↵k)µt + �txt + �t
JX
j=0
�ot�j
+ ⇠t
JX
j=0
�et�j + ✓t
JX
j=0
�qt�j + "t. (8)
14Hooker (2002) uses J = 2 without the contemporaneous term, and Hara, Hiraki, and Ichise (2015) setJ = 3. For our analysis, we employ J = 2, which is preferred to J = 3 by information criterion for the coreinflation. However, the results with J = 3 are qualitatively very similar.
Here,�ot = log(Ot)�log(Ot�1),�et = log(Et)�log(Et�1),�qt = log(Qt)�log(Qt�1), andOt,
Et, and Qt are the oil price index, nominal e↵ective exchange rate, and TOPIX, respectively.15
One problem associated with this extended Phillips curve is that it is formidable, if not
impossible, to consider the three-regime ST model due to the highly nonlinear structure with
many parameters to estimate. Therefore, for this analysis, we restrict the data to between
1996 and 2016 and assume that each coe�cient evolves the following two-regime ST model:16
µt = µ(2) +G2(st; c2, �2)�µ(3) � µ(2)
�
�t = �(2) +G2(st; c2, �2)��(3) � �(2)
�
�t = �(2) +G2(st; c2, �2)��(3) � �(2)
�(9)
⇠t = ⇠(2) +G2(st; c2, �2)�⇠(3) � ⇠(2)
�
✓t = ✓(2) +G2(st; c2, �2)�✓(3) � ✓(2)
�
Judging from the regime dynamics of the previous sections, the assumption of two regimes
is not unreasonable when using the data after 1995 . In addition, we assume that each
coe�cient shares the common transition parameters c2 and �2, as the previous section, to
restrain the number of parameters. Thus, we require the timing and speed of the regime
transition of each parameter to be the same. However, note that this assumption is not
restrictive since we still estimate the coe�cient of each regime, for example µ(i) and ✓(i),
allowing for very di↵erent dynamics for each coe�cient. Finally, like in the previous section,
we impose the sign restrictions that the coe�cient on output gap, oil price, exchange rate,
and the stock price are consistent with the economic theory. Specifically, we assume that the
coe�cients on output gap, oil prices, and stock prices are nonnegative, while the coe�cients
on the exchange rate are nonpositive.17
Figure 3 plots the estimated dynamics of each coe�cient based on the extended three-
regime ST Phillips curve, which is characterized by (8)-(9), for the core inflation.18 As can
be seen, the results demonstrate that the expected inflation experienced a noticeable increase
around the beginning of 2013, which is consistent with the results of the previous section.
The results also indicate that the coe�cient on the output gap and oil price had been positive
throughout the sample, although the oil price became less important in regime 3. However,
the exchange rate turned into an important factor in regime 3 despite the fact that it had no
e↵ect in regime 2. Finally, the results clearly suggest that stock prices played a minor role
throughout the period, particularly in regime 3.
[Insert Figure 3 here]
15More precisely, we normalize each variable to have to have zero mean and unit variance as ab output gapto make each coe�cient easy to compare.
16We call these two regimes regime 2 and regime 3 to correspond with results of the previous section.17If these restrictions are bound for some coe�cients, we replace them with 0 and re-estimate the model.18To save space, the estimates are not reported here, but they are available upon request from the author.
Figure 4 shows the results of the dynamics of each coe�cient in the extended three-regime
ST Phillips curve (8)-(9) for the core2 inflation. As can be seen, the results are qualitatively
similar, except that the oil prices were not important throughout the sample. This is not
surprising, since the core2 inflation is calculated from the CPI, excluding food and energy.
More importantly, the results suggest that the exchange rate became influential in regime 3,
although the e↵ects of stock prices were completely negligible.
[Insert Figure 4 here]
To see these points more clearly, we have calculated the estimate for each factor component
in the extended three-regime ST Phillips curve (8)-(9) and plotted them in Figure 5.19 As can
be seen, the expected core inflation lowered the core inflation by �0.16% in regime 2, while
it elevated the core inflation by 0.25% in regime 3. Similarly, the expected core2 inflation
decreased the core2 inflation by �0.40% in regime 2, while it increased the core2 inflation
by 0.46% in regime 3. Thus, the results demonstrate that the negative expected inflation
was one of the main causes of the deflationary regime between 1996 and 2012; the result also
indicate that changes in expected inflation were one of the key factors in the recent increase
in inflation. Furthermore, the results illustrate that both the output gap and oil prices
played a significant role in determining the core inflation in regime 2, but they became less
important in regime 3. In particular, the results indicate that the recent decline in oil prices
has lowered the core inflation at most 0.1%. Correspondingly, both output and oil prices had
no e↵ect on the core2 inflation in regime 3, although the output gap was relatively influential
in regime 2. On the contrary, the exchange rate a↵ected the core and core2 inflation more
significantly in regime 3 than in regime 2, showing that the rapid depreciation of the yen
after the introduction of the 2% inflation target increased the core (core2) inflation by up
to 0.18% (0.24%), but the appreciation of the yen during the last one year of the sample
lowered it by �0.27% (�0.35%). Finally, the stock prices had little e↵ect on either the core
or the core2 inflations in both regimes 2 and 3.
[Insert Figures 5 here]
In sum, our results are clear-cut. Even if we consider the e↵ects of oil prices, stock
prices, and exchange rates on inflation, expected inflation shows similar dynamics to the
previous section. Specifically, expected inflation has been below 0% and stable until the
end of 2012; it rapidly increased to more than 0% at around the beginning of 2013. Thus,
our results demonstrate that the negative expected inflation was one of the main causes of
the deflationary regime between 1996 and 2012; our results also indicate that changes in
expected inflation were one of the key factors for the recent increase in inflation. In addition,
19For this figure, we have taken the 12-month moving average to filter out the short-run fluctuation.
our results suggest that while the output gap and oil prices were relatively important in
regime 2, the exchange rate played an essential role in explaining the rise and decline of
both core and core2 inflations in regime 3. Finally, it was clear that stock prices were not a
significant determinant of inflation in both regime 2 and regime 3.
4.2 ST Phillips Curve with Multiple Transition Variables
In the previous subsection, we extended the Phillips curve so that the oil prices, stock prices,
and exchange rates could a↵ect the realization of inflation. However, in that model, these
variables could not influence the expected inflation directly, although it is of great interest to
examine the e↵ects of these variables on the expected inflation. Therefore, it is informative
to investigate how the recent depreciation of the yen, decline in oil prices, and surge in stock
prices a↵ect the dynamics of expected inflation regimes. In this subsection, we extend the
benchmark model so that the oil prices, stock prices, and exchange rates can influence the
expected inflation regime.
To this end, we use the benchmark ST Phillips curve model (6) with the extended transi-
tion function (3), including oil prices, stock prices, and exchange rates. More specifically, we
define a transition variable vector as st = (t/T,PJ
j=0 �ot�j�1,PJ
j=0 �qt�j�1,PJ
j=0 �et�j�1)0
and assume that the transition function for the expected inflation can be written as
G(st) =1
1 + exp[��T (s1,t � cT )� �O(s2,t � cO)� �E(s3,t � cE)� �Q(s3,t � cQ)], �T > 0
(10)
Thus, in this model, we can capture the transition of expected inflation depending not only
on time but also on the oil prices, stock prices, and exchange rates. Similar to the model
in the previous subsection, this model may be too complicated to estimate the three-regime
model. Therefore, we restrict the data to between 1996 and 2016, and we assume that there
are only the two regimes, like in the previous subsection.20 In addition, we assume �O = 0 for
the core2 inflation, since it is hard to expect that the oil price a↵ects the expected inflation
of core2 inflation by definition.
Table 3 summarizes the estimation results of the two-regime ST Phillips curve model
(6) with (10) as a transition function for the expected inflation regime.21 As can be seen,
the results of the expected inflation are consistent with the previous results. To be specific,
for the core inflation, the expected inflation is estimated to be negative in regime 2 and
positive in regime 3, although they are not significantly di↵erent from 0. In contrast, for the
core2 inflation, the expected inflation was significantly negative in regime 2 and significantly
20We again call these two regimes regime 2 and regime 3 to make them correspond with the results so far.21As in the previous subsection, we set J = 2 for this analysis. In addition, if the estimate of �i reaches
the upper limit of 200, we set �i = 200 and re-estimate the model. In this case, the parameter’s standarderrors are denoted by NA.
positive in regime 3. The results also indicate that the oil prices significantly a↵ected the
expected inflation regime for the core inflation. Specifically, the positive estimate suggests
that if the oil price has increased over the last three months, then the expected inflation regime
tends to shift from the deflationary regime (regime 2) to the inflationary regime (regime 3).
Thus, our results indicate the possibility that the recent decline in the oil prices pulls back
the current inflation regime to the deflationary regime. Finally, our results show that the
exchange rate played an insignificant role in determining the expected inflation regime for
both inflations, while stock prices had a significant positive impact on the expected inflation.
This greatly contrasts with the results of the previous subsections. Thus, for the realization
of the inflation, the exchange rate matters more; however, for the expected inflation regime,
the stock prices are more important. This is relevant because the exchange rate directly
a↵ects inflation through the price of import goods, while the stock prices should have more
of an e↵ect on the people’s minds, altering the expected inflation.
[Insert Table 3 here]
To see the joint e↵ects of these variables on the expected inflation, Figure 6 plots the
estimated dynamics of expected inflation based on the two-regime ST Phillips curve model
(6) with (10) as a transition function for the expected inflation regime. As can be seen,
the results suggest that the expected inflation had been negative and stable almost all the
time before 2013, but the expected inflation increased rapidly to more than 0.5% around the
beginning of 2013 for both inflation measures. This regime shift was caused by the drastic
changes in the BOJ’s monetary policy, which was captured by the time-trend variable and
the corresponding surge in stock prices. However, the expected inflation occasionally went
back to the deflationary regime even after that. For the core inflation, the oil and stock price
decreases seemed to be equally responsible for this reversion, while the stock price decline
was the main reason for the core2 inflation.
[Insert Figure 6 here]
In sum, the results of this subsection show the robustness of our findings of the shift
in the expected inflation from the deflationary regime to the inflationary regime after the
introduction of the 2% inflation target by the BOJ. In addition, our results indicate the
importance of oil and stock prices in maintaining the inflationary regime. The BOJ tripled
the purchase of ETF in October 2014 and almost doubled it again in July 2016. Our results
suggest that this kind of policy could be e↵ective in preventing the expected inflation regime
from going back to the deflationary regime, which was mainly observed before 2013.
5 Conclusions
Over the last three decades, the Japanese economy has experienced many significant events,
such as the bursting of the bubble economy, the lost two decades, the Lehman and Euro
financial crises, and the introduction of a zero interest rate and inflation targeting monetary
policies. It is quite meaningful to empirically study how expected inflation rates in Japan
have evolved through these events. Along this vein, this paper investigated the possible
regime shifts in expected inflation in Japan over the last three decades and their relation
with monetary policy regimes.
We applied the ST Phillips curve model to identify the number of regimes, characterize
each regime, and estimate the dynamics of expected inflation. Our results indicated that
there were arguably three regimes in the expected inflation in Japan over the last three
decades. In addition, our results suggested that these three regimes reasonably corresponded
to the traditional monetary policy regime between 1985 and 1994 (regime 1), the extremely
low interest rate monetary policy regime between 1995 and 2012 (regime 2), and the inflation
targeting monetary policy regime since 2013 (regime 3).
Our three-regime ST Phillips curve model showed that the expected inflation in regime
1 was relatively high with more than 1.5%, and stable. Nonetheless, the expected inflation
in regime 2 decreased considerably and stayed below 0% most of the time in this regime,
although in the 2000s the BOJ enacted many pioneering monetary policies, such as a zero
interest rate and quantitative easing monetary policies. Thus, those BOJ’s monetary policies
were not enough to escape from the deflationary regime, although they most likely supported
the Japanese economy and prevented the expected inflation from decreasing further. Finally,
the expected inflation in regime 3 revealed a sizable increase, recovering the inflationary
regime. However, our results clearly demonstrated that the expected inflation in regime 3
was significantly smaller than the BOJ’s 2% inflation target for both inflation measures. Thus,
the QQE and the negative interest policies conducted in regime 3 were partially successful
to escape from the deflationary regime, but they were not su�cient to achieve the BOJ’s 2%
inflation target.
In addition, we extended the benchmark model so that the oil prices, stock prices, and
exchange rates could a↵ect inflation. Here, our results indicated that the oil price and
exchange rate had relatively large e↵ects on the core inflation in regime 2 and regime 3,
respectively. On the other hand, the oil prices, stock prices, and exchange rates had little
e↵ect on the core2 inflation in regime 2, although the exchange rates became influential in
regime 3. Thus, our results suggested that the depreciation of the Japanese yen occurred due
to the introduction of the inflation targeting policy by the BOJ played an important role on
the significant increase of inflation in 2013. Furthermore, the recent rebound of the exchange
rates is an important cause of the recent decline in inflation.
Finally, we also considered another type of extended model in which the oil prices, stock
prices, and exchange rates could a↵ect the dynamics of the expected inflation regime. Our
results showed that the oil and stock prices had a significant impact on the expected inflation
regime for the core inflation, while the stock price strongly a↵ected the expected inflation
regime for the core2 inflation. This greatly contrasts with the above results, which show the
importance of the exchange rates in explaining the realization of inflation. More specifically,
our results demonstrated that, even after 2012, the expected inflation regime tended to
move back to the deflationary regime when the oil prices or stock prices decreased markedly.
Therefore, the BOJ’s purchase of ETF could be e↵ective in preventing the expected inflation
from going back to the deflationary regime that was mainly observed before 2013.
References
[1] Chan, K.S. and H. Tong (1986), On Estimating Thresholds in Autoregressive Models,
Journal of Time Series Analysis, 7, 179-190.
[2] De Veirman, Emmanuel (2009), “What Makes the Output-Inflation Trade-o↵ Change?
The Absence of Accelerating Deflation in Japan,” Journal of Money, Credit and Banking
41, pp.1117-1140.
[3] Eitrheim, Øyvind and Timo Terasvirta (1996), “Testing the Adequacy of Smooth Tran-
sition Autoregressive Models,” Journal of Econometrics 74(1), pp.59-76.
[4] Fuhrer, Je↵rey C. and George R. Moore (1995), “Inflation Persistence,” Quarterly Journal
of Economics 110(1), pp.127-159.
[5] Fuhrer, Je↵rey C., Giovanni P. Olivei and Geo↵rey M. B. Tootell (2012), “Inflation Dy-
namics when Inflation is Near Zero,” Journal of Money, Credit and Banking 44, pp.83-122.
[6] Galı, Jordi and Mark Gertler (1999), “Inflation Dynamics: A Structural Econometric
Analysis,” Journal of Monetary Economics 44(2), pp.195-222.
[7] Galı, Jordi, Mark Gertler, and J. David Lopez-Salido (2005), “Robustness of the Esti-
mates of the Hybrid New Keynesian Phillips Curve,” Journal of Monetary Economics 52,
pp.1107-1118.
[8] Granger, C.W.J., and T. Terasvirta (1993), Modeling Nonlinear Economic Relationships,
New York: Oxford University Press.
[9] Hara, Naoko, Kazuhiro Hiraki and Yoshitaka Ichise (2015), “Changing Exchange Rate
Pass-Through in Japan: Does It Indicate Changing Pricing Behavior?,” Bank of Japan
Working Paper Series, 15-E-4, Bank of Japan.
[10] Hooker, Mark A. (2002), “Are Oil Shocks Inflationary? Asymmetric and Nonlinear
Specifications versus Changes in Regime,” Journal of Money, Credit and Banking 34,
pp.540-561.
[11] Inoue, Tomoo and Tatsuyoshi Okimoto (2008), “Were There Structural Breaks in the
E↵ects of Japanese Monetary Policy? Re-evaluating Policy E↵ects of the Lost Decade,”
Journal of the Japanese and International Economies 22(3), pp.320-342.
[12] Kaihatsu, Sohei and Jouchi Nakajima (2015), “Has Trend Inflation Shifted?: An Em-
pirical Analysis with a Regime-Switching Model,” Bank of Japan Working Paper Series,
15-E-3, Bank of Japan.
[13] Lin, Chien-Fu Je↵ and Timo Terasvirta (1994), “Testing the Constancy of Regres-
sion Parameters Against Continuous Structural Change,” Journal of Econometrics 62(2),
pp.211-228.
[14] Luukkonen, Ritva, Pentti Saikkonen and Timo Terasvirta (1988), “Testing Linearity
Against Smooth Transition Autoregressive Models,” Biometrika 75, pp.491-499.
[15] Miyao, Ryuzo (2000), “The Role of Monetary Policy in Japan: A Break in the 1990s?,”
Journal of the Japanese and International Economies 14, pp.366-384.
[16] Roberts, John M. (1997), “Is Inflation Sticky?,” Journal of Monetary Economics 39,
pp.173-196.
[17] Roberts, John M. (2006), “Monetary Policy and Inflation Dynamics,” International
Journal of Central Banking, 2(3), pp.193-230.
[18] Terasvirta, Timo (1994), “Specification, Estimation and Evaluation of Smooth Tran-
sition Autoregressive Models,” Journal of American Statistical Association 89(425),
pp.208-218.
Table 1: Results of the hypothesis testing
Core Core2
LM stat 15.16 65.00
P-value 0.0190 0.0000
LM stat 5.72 13.68
P-value 0.4554 0.0334
LM stat 8.572 8.369
P-value 0.1991 0.2123
1regime vs 2 regimes
2 regimes vs 3 regimes
3 regimes vs 4 regimes
Table 2: Estimation results of bench mark model
Estimate Std. Error Estimate Std. Error
ʅ(1) 1.452 0.231 1.924 0.156
ɴ(1) 0.537 0.267 0.623 0.237
ʅ(2) -0.195 0.152 -0.605 0.106
ɴ(2) 0.171 0.135 0.130 0.081
ʅ(3) 0.338 0.563 0.475 0.215
ɴ(3) 0.186 0.787 0.001 0.521
ɲ1 0.238 0.050 -0.091 0.054
ɲ2 0.144 0.061 0.051 0.052
ʍ 1.421 0.056 1.358 0.049
ɶ1 200 NA 19.14 5.203
c1 0.294 0.010 0.350 0.019
ɶ2 200 NA 200 NA
c2 0.8770 0.0230 0.8906 0.0218
LLH -665.6 -648.6
Core Core2
Table 3: Estimation results of multiple transition variable model
Estimate Std. Error Estimate Std. Error
ʅ(2) -0.2290 0.1531 -0.3974 0.0880
ɴ(2) 0.2272 0.1078 0.1716 0.0833
ʅ(3) 0.5591 0.4085 0.5719 0.2397
ɴ(3) 0.7780 0.8287 0.3182 0.9184
ɶT 200 NA 200 NA
c2 0.8614 0.0116 0.8932 0.0124
ɶO 8.8265 2.8311 0 NA
ɶE -0.0001 1.0841 -0.9865 3.3808
ɶS 8.1270 3.8458 13.0258 4.7553
LLH -437.5 -427.6
Core Core2
Figure 1: Dynamics of transition functions
Figure 2: Dynamics of expected inflation and the slope of the Phillips curve
Figure 3: Dynamics of each coefficient for the core inflation
Figure 4: Dynamics of each coefficient for the core2 inflation
Figure 5: Factor decomposition of the inflations
Figure 6: Dynamics of expected inflation based on the multiple transition variable model